English

The Very General Verra Fourfold is Irrational

Algebraic Geometry 2026-04-17 v1

Abstract

We show that the very general Verra fourfold is irrational, using the Hodge atom framework of Katzarkov--Kontsevich--Pantev--Yu. Two novel points are: a refined analysis of Hodge atoms, based on the involution on the cohomology of XX, and a derivation of the quantum multiplication matrix from the quantum differential operator. This gives the first successful application of the method of Hodge atoms to a space with Picard rank greater than one.

Keywords

Cite

@article{arxiv.2604.14850,
  title  = {The Very General Verra Fourfold is Irrational},
  author = {Aideen Fay},
  journal= {arXiv preprint arXiv:2604.14850},
  year   = {2026}
}
R2 v1 2026-07-01T12:12:23.977Z